Don't we just like to repeat?

So what makes a piece of music beautiful? Most musicologist would argue, the repetition is the key aspect of the beauty. The idea that we take a melody, a motif, a musical idea, we repeat it, we set up the expectation for repetition, and then we either realize it or break the repetition. And that’s a key component of beauty.

When I was a pupil in the drawing class, I hated repetition. No particular aesthetic reason, I simply resisted the boring labor work of drawing the same thing again and again. (What a shame I didn’t know about block printing at that time!) Drawing a repetitive pattern is not spontaneous to most of the children, as opposed to “Draw a face of your daddy.” Besides the daunting labor work most children try to avoid, It also requires a certain level of abstract thinking to engage in this process. Only until the computer entered my working process, and I got better at maths after learning a bit programming language, did I become nerdy about repetitive patterns.

1. Wearing The Mathematician’s Glasses

A mathematician may not be the best person to consult about which wallpaper is better for the bedroom, but we hip people who know how to draw could learn from their abstract thinking. I found their approach a mind-opener to elevate the design.

Mathematicians identified four “operations” (in their term) to transform a basic unit to create the symmetry: translation,  rotationreflection and glide reflection.

Illustration Courtesy of Threads Magazine, Symmetry for Quilters

Illustration Courtesy of Threads Magazine, Symmetry for Quilters

Adobe Illustrator Tips

Transform Again

Holding Alt/Opt key while dragging a motif would duplicate it to the new position. While keeping that duplicated instance selected, click Ctrl/Cmd + D (hotkey for Transform Again) several times will create a line of the motifs evenly distributed.

Ctrl/Cmd + D is one of my favorite shortcuts. Using it creatively in combination any transformation you just defined, could lest you see a repeated result easy and quickly.

Now we're talking about Don't We Just Like to Repeat!

Customized Reflection Axis

Besides reflecting horizontally or vertically from the default center axis, we can also define a custom reflection axis. Select the motif, then call out the Reflect Tool.

Click on the point where you want the axis to be while holding Alt/Opt key. A dialogue pops up and you can define how you want to reflect this motif, then choose “Copy”.

The same technique works with Rotate Tool too.

2. Transforming the Motif

The four operations, Translation, Rotation, Reflection and Glide Reflection, are the starter kit for kaleidoscopic patterns. by mixing up the four basic operations, we can create as many beautiful drawings as we want.

On an abstract level though, says the mathematician, all the seamlessly tile-able patterns can be expressed as one of patterns in the 17 Wallpaper Group. If we use "F" as a motif, for "F" itself is not symmetric in anyway, we could frame all the seamless patterns as below:

Image courtesy of Matt Handler.

"Yeah, geek, but what's the use for us?"

Thanks to Matt Handler, we can use his Mad Pattern templates in Adobe Illustrator. His template is very useful when you want to create a seamless pattern.

Adobe Illustrator Tips

Utilize the Transform Effect

Keep the motif you want to transform selected, then from the main menu, go to Effect > Distort & Transform > Transform... A dialogue will pomp out.

Transform Effect is very useful when you want to apply a transformation to a motif in multiple steps. This effect can be nested too, meaning you could apply the Transformation Effect on a layer or a object that already has this effect applied.

Matt Handle's Mad Pattern Illustrator Template in fact used this technique to apply the 17 Wallpaper Groups transformation rules.

3. Plotting a Grid

Another way of drafting a pattern is, instead of repeating a motif, think about the grid, the big picture first. I learned this technique from Kolam drawing, the South India floor pattern. Most of their patterns are plotted based on a dotted grid system:

Three types of basic grids and their plot

Three types of basic grids and their plot

Image Courtesy of Rmnathan.

Image Courtesy of Rmnathan.

4. Interlocking Patterns

In fact, many of M.C. Escher's intricate tessellation patterns are based on his grid system. He is said to have filled five folio sketchbooks of tessellation drawings - not as the final artwork, but serving as a reference source for him. The seahorse pattern here is one of his 137 tessellation sketches.

Most of his pattern is based on a very simple lattice grid, where he places the animal motifs carefully designed so that the positive and negative spaces interlock.

Image Courtesy of M.C. Escher, from Math & Art of MC Escher

Image Courtesy of M.C. Escher, from Math & Art of MC Escher

5. Scale Symmetry and Fractals

Pattern is an endless topic. The four operations introduced above are used to create patterns that can be tiled seamlessly. I didn't touch the concept "Scale", but that's yet another huge topic. I'll leave it for next time. For now let's just appreciate great arts, and thank God for sending those extraordinarily brilliant human beings to our world.

Image Courtesy of M.C. Escher, from pérolas da madruga